Malory Marin
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View article: Subcoloring of (Unit) Disk Graphs
Subcoloring of (Unit) Disk Graphs Open
A subcoloring of a graph is a partition of its vertex set into subsets (called colors), each inducing a disjoint union of cliques. It is a natural generalization of the classical proper coloring, in which each color must instead induce an …
View article: Subexponential and Parameterized Mixing Times of Glauber Dynamics on Independent Sets
Subexponential and Parameterized Mixing Times of Glauber Dynamics on Independent Sets Open
Given a graph $G$, the hard-core model defines a probability distribution over its independent sets, assigning to each set of size $k$ a probability of $\frac{λ^k}{Z}$, where $λ>0$ is a parameter known as the \emph{fugacity} and $Z$ is a n…
View article: Identifying hard native instances for the maximum independent set problem on neutral atoms quantum processors
Identifying hard native instances for the maximum independent set problem on neutral atoms quantum processors Open
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world …
View article: A structural description of Zykov and Blanche Descartes graphs
A structural description of Zykov and Blanche Descartes graphs Open
In 1949, Zykov proposed the first explicit construction of triangle-free graphs with arbitrarily large chromatic number. We define a Zykov graph as any induced subgraph of a graph created using Zykov's construction. We give a structural ch…
View article: Channel allocation revisited through 1-extendability of graphs
Channel allocation revisited through 1-extendability of graphs Open
We revisit the classical problem of channel allocation for Wi-Fi access points (AP). Using mechanisms such as the CSMA/CA protocol, Wi-Fi access points which are in conflict within a same channel are still able to communicate to terminals.…
View article: Beyond recognizing well-covered graphs
Beyond recognizing well-covered graphs Open
We prove a number of results related to the computational complexity of recognizing well-covered graphs. Let $k$ and $s$ be positive integers and let $G$ be a graph. Then $G$ is said - $\mathbf{W_k}$ if for any $k$ pairwise disjoint indepe…
View article: Three remarks on $\mathbf{W_2}$ graphs
Three remarks on $\mathbf{W_2}$ graphs Open
Let $k \geq 1$. A graph $G$ is $\mathbf{W_k}$ if for any $k$ pairwise disjoint independent vertex subsets $A_1, \dots, A_k$ in $G$, there exist $k$ pairwise disjoint maximum independent sets $S_1, \dots, S_k$ in $G$ such that $A_i \subsete…